Multi-petaled oblique-plane hoop and pipe connector thereof

ABSTRACT

The invention describes a multi-petaled oblique-plane hoop and a pipe connector. The hoop is divided into two groups, and the hoop petals in each group are connected by means of pins, and the pins are parallel to a connecting pipe shaft. The groups are connected by using bolts, and the bolts are vertical to a pipe shaft. Each hoop petal is in a shape of a partial ring stud, in which an arc-shaped groove is formed. The upper surface and the lower surface of the groove are symmetrical partial inner cone surfaces, and the hoop petals are connected to form a clamping chain.

TECHNICAL FIELD

The invention relates to a loop and a pipe connector for the loop and belongs to the mechanical field, being suitable for pipe connection in the petrochemical engineering, chemical engineering, pharmaceutical, electric power, metallurgical and boiler industries.

BACKGROUND

In the industry, pipes are usually connected through flanges or flanged valves. Flanges are bulky, material wasting and difficult to install, but have no good substitutes all the time. For pipes of small calibers below DN50, unions can be used in place of flanges. Compared to the flanges, the unions are easier to install, have a weight 20˜30% of the flange weight, and require 30˜50% lower costs. The union type valves require materials and costs which are lower than the flanged valves by similar extent. Although being only used for civil pipe connection at present, the union type valves will be popularized in the chemical engineering industry sooner or later. The annular-ring seal gasket proposed by the inventor has solved the sealing problem of unions used for chemical engineering. Please see CN 203756982 U and CN 204717181 U. For large-caliber pipes, hoops can be used in place of flanges, but hoops use rubber seals which are only suitable for water pipe connection. Therefore, hoops are only applied in fire-fighting water pipes, foods and pharmaceutics and rarely used in other industries. High-pressure hoops used in the petroleum industry adopt hard seal ring gaskets which have high processing precision requirement and high fabrication costs, thus being unable to popularize.

The existing hoop is mainly used for water pipe connection and composed of a hoop, a long neck flange, a bolt and a seal gasket, as shown in FIG. 1. The hoop usually has 2 petals or 3 petals to the maximum (see the national standard). After being installed, the inner cone surface of the hoop petal and the outer cone surface of the long neck flange fit with each other completely. “b” is the point of tangency in the figure. Suppose that the seal gasket is an asbestos gasket. If leakage is found after a period of use, the seal gasket needs to be tightened. After tightening, the hoop petal shrinks inwardly, and the point of tangency moves from point b to point c. At this time, the diameter of the inner cone circle of the hoop petal on the axial section D-D is larger than the diameter of the outer cone circle of the long neck flange. The same applies on other sections. The two cone surfaces do not closely fit with each other anymore, the inner cone surface of one hoop petal fits with the outer cone surface of the long neck flange only through a line which is in the middle of the inner cone surface of the hoop petal, the two sides of the hoop petal upwarp, and two hoop petals only have two fitting lines. If the gasket seals or the nut cannot be tightened any more when the hoop does not reach the point b, one hoop petal and the cone surface of the long neck flange have two fitting lines which are outside the hoop petal, the hoop petal is convex in the middle, and because the lugs of two adjacent hoop petals are very close to each other, the two fitting lines act like just one fitting line. It can be seen that the existing hoop seal gasket can only be a soft seal, rather than a forced seal gasket like an asbestos gasket and a spiral wound gasket.

In summary, after the existing hoop is installed, the inner cone surface of the hoop petal fits with the outer cone surface of the conical head of the connecting pipe, without any displacement allowed. When the hoop is installed in position, the hoop petals will upwarp if the bolt is excessively tightened. Therefore, only soft seals like rubber O rings and rubber C rings with self-tightening function can be used, largely restricting the hoop application range.

Hoops are also used for high-pressure pipe connection in the petroleum industry. The seal gaskets used are octagonal rings. The hoops are manufactured by installing the hoops and gaskets to form rings and finish-turning the rings. The hoops are expensive and can only be used for small-caliber pipes. Actually, it is pointed out in GB150.3 Pressure Vessels—Part 3: Design that hoop “seal rings shall have self-tightening function” (p281) and thus the seal rings can only be rubber O rings or rubber C rings.

Therefore, the hoops are not popularized in industry, but only popularized by force in fire prevention and water supply and discharge pipes. The seal rings are rubber C rings. Most of the fluid conveyed in pipes in the chemical engineering industry is flammable and explosive media at high temperature. The gaskets are not allowed to be rubber, and thus the existing hoops cannot be applied in the chemical engineering industry.

SUMMARY OF THE INVENTION

On the basis of the traditional hoop, the invention aims to propose a novel hoop and a pipe connector for the hoop: a multi-petaled oblique-plane hoop and a pipe connector for the multi-petaled oblique-plane hoop, which are called a plane hoop and a hoop connector for short. The joint surfaces between the hoop petals and the conical head of a connecting pipe are oblique planes, where seal gaskets like asbestos gaskets, spiral wound gaskets and metal rings can be used. The hoop and the pipe connector can be used for connecting low/medium/high pressure pipes or pipes with flammable and explosive media in place of flanges of over DN50.

The invention adopts the following technical scheme: a multi-petaled oblique-plane hoop, wherein the hoop is divided into two groups, and the hoop petals in each group are connected by means of pins, and the pins are parallel to a connecting pipe shaft. The groups are connected by using bolts, and the bolts are vertical to a pipe shaft. Each hoop petal is in a shape of a partial ring stud, in which an arc-shaped groove is formed. The upper surface and the lower surface of the groove are symmetrical partial inner cone surfaces, and the hoop petals are connected to form a clamping chain.

The taper angle of the inner cone surface of the hoop petal, i.e., the included angle between the normal direction of the inner cone surface and the axial direction of the clamping chain is α=5˜80°, preferably 10˜20°. The hoop petal number N is an even number, which is preferably not higher than the number of the bolts of the flanges of the same caliber, e.g., 4, 6, 8, 10, 12 or 18 petals.

The inner cone surface of each hoop petal is convex in the middle to form a trapezoidal plane which is parallel to the cone surface, i.e., the oblique angle of the plane is equal to the taper angle of the cone surface.

The sum of the trapezoid angles γ formed by extending the two sides of the trapezoidal plane of each hoop petal to the center of circle of the clamping chain is Γ=40˜330°, preferably 180˜300°, and the trapezoid angle of a single hoop petal is γ=Γ/N.

The invention also proposes a pipe connector matching the above mentioned hoop, i.e., a connecting pipe, which is called a long neck flange in the traditional hoop. One end of the connecting pipe is a pipe head, the other end thereof is a convex conical head, and the pipe head is welded with the pipe to be connected, or connected with the latter through thread. The outer taper angle of the conical head is equal to the inner taper angle of the hoop petal, and concave trapezoidal oblique planes parallel to the outer cone surface of the conical head are formed on the outer cone surface through a turning tool. The sum of the trapezoid angles formed by extending the two sides of the trapezoidal oblique plane on the conical head of the connecting pipe to the center of circle of the connecting pipe is B=20˜180°, preferably 90˜120°, and the ratio of the trapezoidal angle of the hoop petal to the trapezoidal angle of the connecting pipe is γ/β≥1.1, preferably γ/β≥2.

The bottom surface of the conical head of the connecting pipe is a sealed surface with a forced seal gasket like an asbestos gasket, a spiral wound gasket and a metal ring with the sealed surface being a plane, a concave-convex surface, a tongue-groove surface, a ring groove surface or a triangular-ring inner groove surface. A soft seal gasket like a rubber O ring and a rubber C ring with self-tightening function can also be used.

The above mentioned clamping chain and connecting pipe are combined to form a new pipe connector: a pipe connector for the multi-petaled oblique-plane hoop, which is called a hoop connector for short. A set of clamping chain and a pair of (two) connecting pipes form a set of hoop connector, a seal gasket is placed between the conical heads of the two connecting pipes, two connecting bolts of the hoop are tightened, and the pipe heads of the two connecting pipes are respectively welded with the pipes on the two sides, so as to complete hoop connector installation.

Beneficial effects: the hoop connector proposed by the invention can be used for connecting a pipe of DN15˜3000, preferably DN50˜700. The working pressure ranges from low pressure to high pressure. The working temperature ranges from subzero temperature to high temperature. The hoop is made of galvanized carbon steel, black carbon steel, phosphatized carbon steel, nickel-plated carbon steel or stainless steel. The connecting pipe is made of carbon steel, stainless steel or another material. The hoop and the connecting pipe are both manufactured by forging and machining blanks, and are mainly used in the chemical engineering industry. The hoop and the connecting pipe can also be forged if being used for civil pipe connection.

The hoop connector proposed by the invention has a weight 20˜30% of the weight of a pair of flanges, except the straight section of the connecting pipe. The connecting pipe has a weight 2.5˜6% of the pair of flanges, except the straight section. The hoop connector is easily manufactured with low size requirements except for the taper angle. After the hoop connector is marketized, the low-pressure carbon steel hoop connector costs a half of a flange, and the medium/high pressure hoop connector is more advantageous in the price. The stainless steel hoop connector costs 20˜30% of the price of the stainless steel flange. The hoop connector can be used for valve manufacturing. The flanges on the two sides of a valve are replaced with the connecting pipe which is connected with a pipe through the pipe connector, greatly reducing the manufacturing cost and the price of the valve. Popularization of the hoop connector of the invention will lead a revolution in the industrial pipe valve industry and pipe connection field, and has great significance to the development of modern industry and national economy.

BRIEF DESCRIPTION OF DRAWINGS

In FIG. 1, A is the installation drawing of the traditional hoop, and B is the partially enlarged drawing of A.

FIG. 2 is the three-dimensional diagram of the hoop connector, in which A is a nose-end hoop, B is an ear-end hoop and C is the assembly drawing.

FIG. 3 is the three-dimensional projection drawing of the hoop connector assembly, in which A is the connecting pipe, B is the ear-end hoop and C is the nose-end hoop.

FIG. 4 is the cross-section drawing of the hoop connector, in which 1 is the connecting pipe, 2 is the seal gasket, 3 is the hoop, and 4 is the lower connecting pipe.

FIG. 5 is the connecting pipe marking graph, in which A and B are respectively the vertical cross-section drawing and the top view of the upper connecting pipe, C is a partially enlarged drawing of B, and D and E are respectively the top view and the vertical cross-section drawing of the lower connecting pipe.

FIG. 6 is the marking graph of a four-petal hoop, in which A and B are respectively the vertical cross-section drawing and a partially enlarged top view of A, C and D are respectively the cross-section drawings of the A-A left and right parts in A, E and F are respectively the two cross-section drawings of two parts in C, and G and H are respectively the cross-section drawings of two parts in D.

FIG. 7 is the marking graph of a six-petal hoop, in which A and B are respectively the vertical cross-section drawing and a partially enlarged top view of A, C and D are respectively the cross-section drawings of the left and right parts and upper and lower parts in A, and E and F are respectively the two cross-section drawings of two parts in C and D.

DETAIL DESCRIPTION OF THE EMBODIMENTS 1. Naming

The invention is a novel product. Before description, the product and components thereof must be named, as shown in FIGS. 2-7.

In the invention, the hoop is divided into at least four petals, and the cone surface fitting of the traditional hoop is replaced with oblique-plane fitting. The invention is officially called the multi-petaled oblique-plane hoop, the plane hoop for short. The traditional hoop is called the cone hoop for short. The part of the pipe connector of the hoop welded with a pipe is called the long neck flange in the existing standards and literatures, and called the connecting pipe herein. The end of the connecting pipe connected with the pipe is called the butt-welded end, and the other end connected with the hoop is called the conical head.

The pipe connector of the hoop is composed of four parts, the hoop, the connecting pipe, the bolts and the pins, among which the hoop and the connecting pipe are the main parts and the bolts and the pins are connecting parts (accessories). The hoop is divided into two types, an edge hoop and a middle hoop. The edge hoop is divided into a nose-end hoop and an ear-end hoop, and the nose-end hoop, the ear-end hoop and the middle hoop are also called single hoops. The hoop petal number is the multiple of 2 (even number), which is at least 4. FIGS. 2 and 3 are the three-dimensional drawing and the three-dimensional projection drawing of the pipe connector of the four-petal hoop, in which A is the nose-end hoop, B is the ear-end hoop and C is the assembly drawing. The pipe connector assembly of the hoop is called the hoop connector for short. A lug is formed at one end of the edge hoops (A and B), a pin nose is formed at the other end of the nose-end hoop (A), and a pin ear is formed at the other end of the ear-end hoop (B). In a four-petal hoop, one nose-end hoop and one ear-end hoop are connected through the pin to form a group of hoop, two groups of hoops are connected through the bolt to form a whole body, which is called the clamping chain herein. The clamping chain and the connecting pipe form the hoop connector.

FIG. 7 is a six-petal hoop which is divided into two groups, each comprising three petals. The nose-end hoop and the ear-end hoop are on the two sides of each group and the middle hoop is in the middle of each group. The pin nose is at one end of the middle hoop, the pin ear is at the other end thereof, and the middle hoop is connected with the end hoop through the pin. The clamping chain formed by a hoop with at least six petals is composed of the three types of single hoops, the nose-end hoops, the ear-end hoops and the middle hoops. The hoop is manufactured only by using three types of dies.

A set of clamping chain and a pair of (two) connecting pipes form a set of pipe connector, the conical bottoms of the two connecting pipes are sealing surfaces, the sealing surfaces and the seal gaskets can be various types, the pipe heads of the two connecting pipes are respectively welded with the pipes on the two sides, or connected with the latter through thread.

The clamping chain is made of metal like carbon steel and stainless steel, is manufactured by forging and machining blanks, is resistant to high temperature and high pressure, and can be used for flammable and explosive media.

The pipe connector of the hoop can be used for valve connection, i.e., the flange on the traditional flange-connected valve is replaced with the connecting pipe, and the valve is connected with the pipe through the clamping chain.

The pipe connector of the hoop adopts the forced seal gasket, is sized according to chemical engineering and petrochemical engineering design standards, and is used for connecting pipes and equipment with flammable and explosive medium/high-pressure media.

In the pipe connector of the hoop, the hoop can also be manufactured by forging, the pipe heads of the connecting pipes are welded with the pipes connected with the latter through thread, and the gasket is the forced seal gasket or the soft seal gasket. The hoop is used for connecting civil low-pressure pipes with non-inflammable media.

The pipe connector of the hoop (hoop connector) has a connecting pipe caliber of DN15˜3000, preferably DN50˜700.

2. Definition

The hoop connector is a new product which is mainly used for chemical engineering, petroleum, power generation, smelting and other industrial fields in place of the large-caliber flange of over DN50. The hoop connector is required to be designed according to the specifications of national standards on pressure vessels and on metallic industrial pipings. Before design formula derivation, all the parts are named and symboled, as shown in the attached drawings.

b—effective width of the seal gasket;

C₁—negative deviation of pipe wall thickness of the butt-welded end of the connecting pipe, C₁=12.5%;

C_(Dn)—bow length of the bow formed by the oblique plane of the conical head of the connecting pipe on the inscribed circle D_(n), the circle diameter being D_(n)+2v_(D) in calculation;

C_(Dw)—bow length of the bow formed by the oblique plane of the conical head of the connecting pipe on the circumscribed circle D_(w);

C_(En)—bow length of the bow formed by the oblique plane of the hoop on the inscribed circle D_(n), the circle diameter being D_(n)+2v_(E) in calculation;

C_(Ew)—bow length of the bow formed by the oblique plane of the hoop on the circumscribed circle D_(w);

D_(i)—inner diameter of the butt-welded end of the connecting pipe;

D₀—outer diameter of the butt-welded end of the connecting pipe;

D₁—diameter of the circle formed by intersection of the transition arc between the connecting pipe and the cone surface and the cone surface, D₁=D₀+2r₁(1−sin α);

D_(n)—inscribed circle diameter, i.e., diameter of the point of tangency of the conical head of the connecting pipe and the caliber of the clamping chain;

D_(w)—circumscribed circle diameter, i.e., bottom diameter of the conical head of the connecting pipe;

D_(G)—effective diameter of the sealing surface;

d₁—min. cross section diameter of the stud;

d₂—bolt hole diameter;

d₃—pin diameter;

d₄—pin hole diameter;

d₅—outer diameter of the pin ear;

E_(i)—inner diameter of the hoop;

E_(o)—outer diameter of the hoop;

f_(n)—straight section height of the hoop hole, i.e., hoop thickness at the inner point of tangency;

f_(w)—thickness of the point of tangency of the hoop, i.e., hoop thickness at the outer point of tangency;

g_(D)—distance between the cone surface and the oblique plane of the conical head of the connecting pipe;

g_(E)—distance between the cone surface and the oblique plane of the hoop;

Δ_(g)—distance between the oblique plane of the conical head of the connecting pipe and the oblique plane of the hoop after the hoop connector is assembled;

h_(n)—thickness of the point of tangency of the conical head of the connecting pipe, i.e., thickness of the conical head of the connecting pipe at the inner point of tangency;

h_(w)—stud section height of the conical head of the connecting pipe, i.e., thickness of the conical head of the connecting pipe at the outer point of tangency;

La—length of the lug arm of force;

Lw—lug width;

Ln—lug thickness;

m—gasket factor without dimension;

N—hoop petal number;

n_(b)—safety factor of the tensile strength of the material;

n_(s)—safety factor of the yield strength of the material;

PN—nominal pressure, i.e., max. design working pressure (bar);

p—internal pressure (MPa), p=(PN+1)/10;

r₁—radius of the transition arc between the connecting pipe and the cone surface;

r₂—radius of the internal processed transition arc, i.e., the internal chamfer, being 1˜2 mm;

r₃—radius of the external processed transition arc, i.e., the external chamfer, being 0.5˜1 mm;

u₁—pin ear height;

u₂—pin nose height;

v_(D)—bow height of the bow formed by the oblique plane of the conical head of the connecting pipe on the circumscribed circle;

v_(E)—bow height of the bow formed by the oblique plane of the hoop on the inscribed circle;

y—specific sealing pressure of the gasket (MPa);

α—taper angle or oblique angle, i.e., included angle between the cone surface and the cone bottom and included angle between the normal direction of the cone surface and the axial direction of the cone surface, comprising the taper angle between the outer cone surface of the connecting pipe head and the inner cone surface of the hoop and the included angle between the oblique plane of the connecting pipe and the axial cross section, and the included angle between the oblique plane of the hoop and the axial cross section, with the four angles being equal to each other;

B—sum of N trapezoidal angles of the conical head of the connecting pipe;

β_(w)—trapezoidal angle of the connecting pipe, i.e., trapezoidal angle formed by extending the two sides of the trapezoidal oblique plane of the conical head of the connecting pipe to the center of circle of the connecting pipe, with the circumscribed circle D_(w), as the reference and β=B/N;

β_(n)—trapezoidal angle of the connecting pipe, with the inscribed circle D_(n) as the reference;

Γ—sum of the trapezoidal angles of the N single hoops of the clamping chain;

γ_(n)—trapezoidal angle of the hoop formed by extending the two sides of the trapezoidal oblique plane of the single hoop to the center of circle of the clamping chain, with the inscribed circle D_(n) as the reference and γ=Γ/N;

γ_(w)—trapezoidal angle of the hoop, with the circumscribed circle D_(w) as the reference;

δ_(D)—wall thickness of the butt-welded end of the connecting pipe;

δ_(E)—wall thickness of the cylinder section of the hoop;

ΔC—bow length margin, i.e., the length difference between the bow length of the oblique plane of the hoop and the bow length of the oblique plane of the conical head of the connecting pipe on the same circumference after installation, and the length difference on each side;

ΔL—hoop connector distance, i.e., distance between the hole edge of the clamping chain and the bottom line on the oblique plane of the conical head of the connecting pipe;

μ—friction angle, i.e., steel-steel μ=5˜8°, being μ1=5° to the min. and μ2=8° to the max.;

σ_(b1)—tensile strength of the connecting pipe material (MPa);

σ_(b2)—tensile strength of the hoop material (MPa);

σ_(s3)—yield strength of the bolt material and the pin material (MPa);

[σ]_(b1)—allowable stress of the connecting pipe material (MPa);

[σ]_(b2)—allowable stress of the hoop material (MPa);

[σ]_(s3)—allowable stress of the bolt material and the pin (shaft) material (MPa);

φ—wearing coefficient, which can be φ=0.8; a groove weld is designed at the butt-welded end of the connecting pipe;

ω—bow length ratio of the bow length of the oblique plane of the hoop and the oblique plane of the conical head of the connecting pipe on the same circumference.

3. Fit Dimension

(1) Trapezoidal Angle

The trapezoidal angle is the short form of the trapezoidal angle formed by extending the two sides of the trapezoidal oblique plane to the center of circle. Actually, the two sides of the oblique plane are not straight lines, but approximate straight lines. the area of the oblique plane of the connecting pipe is specified to be ¼ of the total area of the outer cone of the connecting pipe, namely, the sum of the trapezoidal angles of the connecting pipe is B=90°; with the cylinder section diameter D_(w) of the conical head of the connecting pipe as the reference, the included angle of a single oblique plane on the conical head of the connecting pipe is:

$\begin{matrix} {\beta_{w} = \frac{90}{N}} & \text{(3-1)} \end{matrix}$

The design ensures that the contact surface of the hoop connector (the oblique plane of the hoop and the connecting pipe) is much bigger than the contact surface of the flange connector (between the flange and the bolt), avoiding flange warping and correction of the nominal gasket width b₀; namely, b=b₀.

The sum of the trapezoidal angles of the hoop is Γ. Through comparison among different design proposals, the sum is preferably Γ=180˜300°; with the hoop hole diameter D_(n) as the reference, the included angle of the oblique plane of each hoop is:

$\begin{matrix} {\gamma_{n} = \frac{\Gamma}{N}} & \text{(3-2)} \end{matrix}$

In consideration of tolerance, processing error and installation displacement, to ensure that the oblique plane of the hoop completely fits with the oblique plane of the connecting pipe, preferably, γ/β≥2.

(2) Distance Between Oblique Plane and Cone Surface

As shown in FIG. 5, the bow height v_(D) of the bow formed by the oblique plane of the conical head of the connecting pipe on the circumscribed circle D_(w) is:

$\begin{matrix} {V_{D} = {\frac{D_{w}}{2}\left( {1 - {\cos\frac{\beta_{w}}{2}}} \right)}} & \text{(3-3)} \end{matrix}$

The distance g_(D) between the oblique plane and the cone surface of the conical head of the connecting pipe is:

$\begin{matrix} {g_{D} = {\frac{D_{w}}{2}\left( {1 - {\cos\frac{\beta_{w}}{2}}} \right)\mspace{14mu}\tan\mspace{14mu}\alpha}} & \text{(3-4)} \end{matrix}$

As shown in FIG. 6, the bow height v_(E) of the bow formed by the oblique plane of the hoop on the inscribed circle D_(n) is:

$\begin{matrix} {v_{E} = {\frac{D_{n}}{2}\left( {1 - {\cos\frac{\gamma_{n}}{2}}} \right)}} & \text{(3-5)} \end{matrix}$

The distance g_(E) between the cone surface and the oblique plane of the hoop is:

$\begin{matrix} {g_{E} = {\frac{D_{n}}{2}\left( {1 - {\cos\frac{\gamma_{n}}{2}}} \right)\mspace{14mu}\tan\mspace{14mu}\alpha}} & \text{(3-6)} \end{matrix}$

After the hoop connector is assembled, the distance Δg between the oblique plane of the conical head of the connecting pipe and the oblique plane of the hoop is:

Δg =g _(E) −g _(D)  (3-7)

The design requires that Δg is as large as possible and is not lower than 0.7 mm; namely, the two cone surfaces have the possibly largest distance.

Since the oblique plane is parallel to the cone surface and g_(D) is equal at all the positions, v_(D) is also equal at all the positions. The project curve of the sides of the trapezoidal oblique plane can be drawn, which is similar to a straight line.

(3) Bow Length Ratio

As shown in FIG. 5, the bow height C_(Dw) of the bow formed by the oblique plane of the conical head of the connecting pipe on the circumscribed circle D_(w) (cone bottom circle) is:

$\begin{matrix} {C_{Dw} = {D_{w}\mspace{14mu}\sin\mspace{14mu}\frac{\beta_{w}}{2}}} & \text{(3-8)} \end{matrix}$

Since the oblique plane is parallel to the cone surface and g_(D) is equal at all the positions, v_(D) is also equal at all the positions. It can be derived that the trapezoidal angle βn of the conical head of the connecting pipe on the inscribed circle D_(n) (hole circle of the clamping chain) is:

$\begin{matrix} {\beta_{n} = {2\mspace{14mu}{\cos^{- 1}\left\lbrack {1 - {\frac{D_{w}}{D_{n} + {2v_{D}}}\left( {1 - {\cos\frac{\beta_{w}}{2}}} \right)}} \right\rbrack}}} & \text{(3-9)} \end{matrix}$

The bow length c_(Dn), of the bow formed by the oblique plane of the conical head of the connecting pipe on the inscribed circle is:

$\begin{matrix} {C_{Dn} = {\left( {D_{n} + {2v_{D}}} \right)\mspace{14mu}\sin\frac{\beta_{n}}{2}}} & \text{(3-10)} \end{matrix}$

Similarly, the bow length c_(En) of the bow formed by the oblique plane of the hoop on the inscribed circle is:

$\begin{matrix} {C_{En} = {\left( {D_{n} + {2v_{E}}} \right)\mspace{14mu}\sin\frac{\gamma_{n}}{2}}} & \text{(3-11)} \end{matrix}$

The trapezoidal angle γw of the hoop on the circumscribed circle is:

$\begin{matrix} {\gamma_{w} = {2\mspace{14mu}{\cos^{- 1}\left\lbrack {1 - {\frac{D_{n} + {2v_{E}}}{D_{w}}\left( {1 - {\cos\frac{\gamma_{n}}{2}}} \right)}} \right\rbrack}}} & \text{(3-12)} \end{matrix}$

The bow length c_(Ew) of the bow formed by the oblique plane of the hoop on the circumscribed circle is:

$\begin{matrix} {C_{Ew} = {D_{w}\mspace{14mu}\sin\frac{\gamma_{w}}{2}}} & \text{(3-13)} \end{matrix}$

The bow length ratios of the hoop to the conical head of the connecting pipe on the inscribed and circumscribed circles are respectively:

$\begin{matrix} {\omega_{n} = \frac{C_{En}}{C_{Dn}}} & \text{(3-14)} \\ {\omega_{w} = \frac{C_{Ew}}{C_{Dw}}} & \text{(3-15)} \end{matrix}$

The bow length margins of the hoop and the conical head of the connecting pipe on the inscribed and circumscribed circles are respectively:

$\begin{matrix} {{\Delta\; C_{n}} = \frac{C_{En} - C_{Dn}}{2}} & \text{(3-16)} \\ {{\Delta\; C_{w}} = \frac{C_{Ew} - C_{Dw}}{2}} & \text{(3-17)} \end{matrix}$

The bow length ratio ω and the bow length margin ΔC reflect the fit reliability of the oblique plane of the hoop and the oblique plane of the conical head of the connecting pipe. For the hoop connector of at least DN50, the design requires ω≥2 and ΔC≥10 mm. The bow length ratio co of the hoop to the connecting pipe is very similar to the trapezoidal angle ratio, i.e., ω≈γ/β≥2.

(4) Hoop Connector Distance

The diameter of the circle at the point of tangency on the center line of the oblique plane of the conical head of the connecting pipe is D_(n), and the diameter of the hoop hole is also D_(n). The diameter of the circle formed by intersection of the transition arc r₁ between the outer diameter of the connecting pipe and the cone surface and the cone surface is D₁, and the top line of the trapezoid on the oblique plane of the conical head of the connecting pipe intersects with the circle D₁. The distance between the hole edge (circle D_(n)) of the clamping chain and the top line (circle D₁) of the trapezoid on the oblique plane of the conical head of the connecting pipe is called the hoop connector distance ΔL. It can be derived from FIG. 5 that:

$\begin{matrix} {{\Delta\; L} = {\frac{D_{n} - D_{1}}{2} - v_{D}}} & \text{(3-18)} \end{matrix}$

According to the design, ΔL=4˜6 mm; ΔL shall be larger for the large-caliber hoop connector.

4. Stress Analysis

The following design calculation formula mainly refers to the standard explanations in the national standard GB 150-2011 Pressure Vessels, the national standard GB 150.14˜2.11 Pressure Vessels, the national standard GB 50316-2000 Design Code for Industrial Metallic Piping and the national standard in the chemical industry HG/T 20582-2.11 Specification of Strength Calculation for Steel Chemical Vessels.

4.1 Axial Load

(1) The tension F_(i) acted by the internal pressure on the axial cross section of the connecting pipe is:

$\begin{matrix} {F_{i} = {2 \times \frac{\pi}{4}D_{i}^{2}p}} & \left( {4\text{-}1} \right) \\ {F_{i} = {\frac{\pi}{2}D_{i}^{2}p}} & \; \end{matrix}$

(2) The axial tension F_(G) acted by the internal pressure on the hoop and the conical head of the connecting pipe is:

$\begin{matrix} {F_{G} = {\frac{\pi}{2}D_{G}^{2}p}} & \left( {4\text{-}2} \right) \end{matrix}$

(3) The axial pre-tensioning force F_(m) of the gasket is:

F_(m)=πD_(G)by  (4-3)

When the self-tightening seal gasket is used, F_(m)=0.

In the formula, b=b₀, because no flange warping occurs on the conical head of the connecting pipe of the clamping chain.

(4) The total axial tension on the hoop in the operating state is:

The pressure vessel standards of different countries are based on the research results achieved in 1940s, in which the pressure stress on the sealing surface in the operating state is believed to be 2 m times of the design pressure p, namely:

F_(p)=2πD_(G)bmp  (4-4)

Where, m is the gasket factor which is determined according to the gasket material, type and size. When the self-tightening seal gasket is used, F_(p)=0.

The axial tensile force Ft in the operating state is the sum of the axial force FG generated by the medium pressure and the axial force F_(p) generated by the sealing pressure stress necessary in the gasket operating state, and can be expressed as:

$\begin{matrix} {F_{t} = {{F_{G} + F_{p}} = {{\frac{\pi}{2}D_{G}^{2}p} + {2\;\pi\; D_{G}{bmp}}}}} & \left( {4\text{-}5} \right) \\ {F_{t} = {\frac{\pi}{2}D_{G}{p\left( {D_{G} + {4b\mspace{14mu} m}} \right)}}} & \; \end{matrix}$

4.2 Radial Load

(1) The internal radial pressure F_(Dj) generated when the gasket is pre-tightened is:

F _(mj)=πD _(G) by tan(α+μ₂)  (4-6)

(2) The total external radial pressure F_(ij) on the hoop in the operating state is:

$\begin{matrix} {F_{tj} = {\frac{\pi}{2}D_{G}{p\left( {D_{G} + {4b\mspace{14mu} m}} \right)}{\tan\left( {\alpha - \mu_{1}} \right)}}} & \left( {4\text{-}7} \right) \end{matrix}$

The steel-steel friction coefficient is f=0.1˜1.5, and the friction angle is μ=tan⁻¹f=5.71˜8.53°≈5˜8°. To guarantee reliable calculation result, the max. value μ₂=8° is used during pre-tightening, and the min. value μ₁=5° is used in the operating state; namely, the stress is the max. possible value.

4.3 Bolt and Pin Load

On any radial cross section of the hoop, the total tension to the two sides is

$\frac{2}{\pi}$

times of the radial pressure. The tension on the two opposite bolts of the hoop (total bolt load) can be calculated accordingly, and is equal to the total load on the two opposite pairs of pins of the hoop.

(1) The total bolt load F_(mM) in the pre-tightening state is:

F _(mM)=2D _(G) by tan(α+μ₂)  (4-8)

(2) The total bolt load F_(tm) in the operating state is:

F _(tM) =D _(G) p(D _(G)+4bm)tan(α−82 ₁)  (4-9)

When the bolt size is calculated, the larger value in F_(mM) and F_(tM) is used; namely:

F_(M)=max(F_(mM), F_(tM))  (4-10)

4.4 Explanation

In the existing pipe connector of the hoop, the cone surfaces of the hoop and the long neck flange can be fit in only one way-complete fit, which cannot be changed, with the bolts only playing the fixing function. Therefore, the stress analysis and strength calculation formula in the standards and the literatures are all based on false assumption.

In GB 150.3, a pre-loading state is also regulated for hoop strength calculation. In the pre-tightening state, the two sealing surfaces of the hoop connector approach to each other, the outer cone surface of the long neck flange moves outward relative to the inner cone surface of the hoop, and generates an inward friction force F on the cone surface of the hoop. In the operating state, the two sealing surfaces tend to separate, the outer cone surface of the long neck flange moves inward relative to the inner cone surface of the hoop, the direction of the friction force on the contact surface between the hoop and the long neck flange is opposite to the pre-tightening direction, and generates an outward friction force F on the cone surface of the hoop. When the pre-tightening state is switched to the operating state, the friction force F on the oblique plane of the hoop turns outward from inward. When the medium pressure rises, at the moment when the two sealing surfaces are about to separate, the friction force on the oblique plane of the hoop is still inward, and is called the pre-loading state. The relation between the bolt load and the axial stress can be calculated by replacing (α−μ₁) in formula (4-9) with (α+μ). Actually, this is only applicable for a feature in the production-misoperation at the beginning leads to excessive instantaneous pressure. This condition only easily occurs to the small-caliber pipe of no more than DN15˜25, while the hoop is only applicable for the connection of the large-caliber pipe of at least DN50, and thus the above mentioned condition does not happen to the hoop, or hardly happens.

In GB 150.3, the axial load Fp acted by the internal pressure on the hoop and the conical head of the connecting pipe is:

$\begin{matrix} {F_{G} = {\frac{\pi}{4}D_{G}^{2}p}} & \left( {4\text{-}2a} \right) \end{matrix}$

This is the single-side axial stress acted by the internal pressure on the hoop and the conical head of the connecting pipe, and is obviously wrong. GB 150.1 specifies that the safety factor of the tensile strength of carbon steel and low-alloy steel is n_(b)=2.7, and the safety factor of the yield strength is n_(s)=1.5, except the bolts; the safety factor of the yield strength of the carbon steel bolts is n_(sm)=2.7. n_(sm)/n_(s)=1.8, which increases the safety factor of the yield strength of the bolts. The increase is actually a compensation for the error in formula (4-2a). The axial load of the internal pressure is calculated by formula (4-2), and the safety factor of the bolt yield strength is set to 1.5. The calculation result is the same as the result obtained by using GB 150.3 but more reliable. In this way, the special regulations on the safety factor of the bolt materials are avoided, and the design calculation method is simplified.

5. Size Calculation

The existing design calculation formulas for the hoop sizes are very complex. For example, the number of calculation formulas is up to 37 in GB 150.3. It is supposed that the area of the oblique plane of the connecting pipe is ¼ of the area of the outer cone of the connecting pipe. To calculate the thickness of the conical head of the connecting pipe at the point of tangency, only the strength of ¼ of the circumference of the point of tangency is calculated, and the other ¾ of the circumference can play a reinforcing function. Therefore, to calculate the sizes of the hoop and the connecting pipe, only the wall thickness δ of the connecting pipe, the effective thickness hn of the conical head of the connecting pipe at the point of tangency and the thickness fw of the hoop at the point of tangency are calculated, without considering the bending and deformation of the cone surfaces of the conical head of the connecting pipe and the hoop, thus greatly simplifying the design calculation process.

5.1 Wall Thickness of Connecting Pipe

The existing pipe wall thickness calculation formulas are simplified approximate formulas which are very complex and obtained before emergence of computers and calculators. According to stress balance, the accurate calculation formula of the pipe wall thickness can be obtained:

$\begin{matrix} {\delta_{D} = {\frac{D_{o}}{2{\varnothing\left( {1 - C_{1}} \right)}}\left( {1 - \sqrt{\frac{1}{1 + {2{p/\lbrack\sigma\rbrack_{b1}}}}}} \right)}} & \left( {5\text{-}1} \right) \end{matrix}$

The calculation result of the above formula is the same as the calculation result of the formula in GB 50316.

5.2 Hoop Wall Thickness

Suppose that the sum of the gap angles at the bolt lugs and the pins of the clamping chain is 60°, i.e., the total arc perimeter of N hoops is 300/360 of the perimeter of the clamping chain. According to force balance, it can be derived that:

$\begin{matrix} {\frac{F_{t}}{\frac{\pi}{4}\left( {E_{o}^{2} - E_{i}^{2}} \right) \times \frac{5}{6}} = \lbrack\sigma\rbrack_{b2}} & \left( {5\text{-}2} \right) \\ {\delta_{E} = {{0.5}\left( {\sqrt{E_{i}^{2} + \frac{2.4p{D_{G}\left( {D_{G} + {4bm}} \right)}}{\lbrack\sigma\rbrack_{b2}}} - E_{i}} \right)}} & \; \end{matrix}$

When the pin ears and the bolt lugs are designed, the total empty angles of the clamping chain shall be less than 60°.

5.3 Thickness of Conical Head of Connecting Pipe at Point of Tangency

According to force balance, it can be derived that:

$\begin{matrix} {{\frac{F_{t}/2}{\frac{\pi\; D_{f}h_{Df}}{4}} = {0.8\lbrack\sigma\rbrack}_{b1}}{h_{Df} = \frac{F_{t}}{04\;\pi\;{D_{f}\lbrack\sigma\rbrack}_{b1}}}} & \left( {5\text{-}3} \right) \end{matrix}$

0.8[σ]_(b1) is the allowable shear stress.

5.4 Thickness of Hoop at Point of Tangency

$\begin{matrix} {h_{Et} = \frac{F_{t}}{0.4\pi\;{D_{t}\lbrack\sigma\rbrack}_{b2}}} & \left( {5\text{-}4} \right) \end{matrix}$

5.5 Bolt

(1) Stud Diameter

For the single-lug hoop, according to force balance, it can be derived that:

$\begin{matrix} {\frac{F_{M}}{2 \times \frac{\pi}{4}d_{1}^{2}} = \lbrack\sigma\rbrack_{s3}} & \left( {5\text{-}5} \right) \\ {d_{1} = \sqrt{\frac{2F_{M}}{{\pi\lbrack\sigma\rbrack}_{s3}}}} & \; \end{matrix}$

For the double-lug hoop, the calculation formula is:

$\begin{matrix} {d_{1} = \sqrt{\frac{F_{M}}{{\pi\lbrack\sigma\rbrack}_{s3}}}} & \left( {5\text{-}6} \right) \end{matrix}$

(2) Lug Calculation

The bending strength of the hoop lugs. The total load of the two opposite pairs of bolts is borne by 4 lugs. The following formula can be derived:

$\begin{matrix} {\lbrack\sigma\rbrack_{S3} = {{0.7}5F_{M}\frac{L_{a}}{L_{w}L_{h}^{2}}}} & \left( {5\text{-}7} \right) \\ {L_{h} = \sqrt{\frac{0.75F_{ML_{a}}}{{L_{w}\lbrack\sigma\rbrack}_{S3}}}} & \left( {5\text{-}8} \right) \end{matrix}$

Suppose that the arm of force L_(w)=circumscribed circle diameter of the nut+5˜6. The lug width is L_(a), and set L_(a)=0.8E for the single lug, and L_(a)=1.5×circumscribed circle diameter of the nut for the double lugs. The bolt caliber is d₂=1.2d₁.

5.6 Pin

(1) Pin Diameter

Each pin has four shearing surfaces. According to force balance, it can be derived that:

$\begin{matrix} {{\frac{F_{M}}{2 \times \frac{\pi}{4}d_{3}^{2} \times 4} = {0.8\lbrack\sigma\rbrack}_{b3}}{d_{3} = \sqrt{\frac{F_{M}}{16{\pi\lbrack\sigma\rbrack}_{b3}}}}} & \left( {5\text{-}9} \right) \end{matrix}$

(2) Pin Ear and Pin Nose (Connectors at Two Ends of Each Hoop)

Suppose that the hole diameter is 1.2 times of the pin diameter, and then d₄=1.2d₃d₄=1.2d₃. Suppose that the pin ear height is u₁u₁, and the pin nose height is u₂u₂. Set u₂=2u₁u₂=2u₁ and u₂+2u₁=0.8Fu₂+2u₁=0.8F, and thus u₁=0.2Fu₁=0.2F. According to force balance, it can be derived that:

$\begin{matrix} {{\frac{F_{M}}{\left( {d_{5} - d_{4}} \right) \times 0.4F \times 2 \times 2} = \lbrack\sigma\rbrack_{b4}}{d_{5} = {{{1.2}d_{4}} + \frac{F_{M}}{{1.6}{F\lbrack\sigma\rbrack}_{b4}}}}} & \left( {5\text{-}10} \right) \end{matrix}$

5.7 Material Safety Factor

To calculate the allowable stress of the material, the safety factor of the tensile strength n_(b) and the safety factor n_(s) of the yield strength of the material are necessary. In GB 150, it is pointed out that “the safety factors currently used in safety regulations and technical standards on pressure vessels are extensive. Many details rely on the safety factors, resulting in the condition that the safety margins of devices or equipment cannot be accurately evaluated”. The idea of the American dynamic safety factor introduced in GB 150 is used herein. The lower safety factors among different countries, British standards are used. For pipes of DN≤15 and PN≤100, a factor of 2 is multiplied (where misoperation and over pressure occur the most easily); for pipes of DN20˜25 and PN≤40, a factor of 1.5 is multiplied; for pipes of DN32˜50 and PN≤40, a factor of 1.2 is multiplied.

TABLE 5-1 Material safety factors in British standards Tensile Strength Yield Strength Material n_(b)n_(b) n_(s)n_(s) Carbon steel and low-alloy steel 2.35 1.5 Austenitic stainless steel 2.5 1.5

5.8 Material Parameters

(1) Mechanical Properties

The mechanical properties of the materials used in the embodiment of the invention come from GB 150.2-2011 and GB/T 1220-2000. See Table 5-2.

TABLE 5-2 Mechanical properties of steel forged pieces (MPa) Material 20# 35# 16Mn 30CrMo 304 321 316 Tensile 410 510 480 620 520 520 520 strength σ_(b)σ_(b) Yield 235 265 305 440 strength σ_(s)σ_(s)

(2) Gasket Factor

In the embodiment of the invention, the seal gasket is the stainless steel-graphite spiral wound gasket, with the gasket factor of m=3 and the specific gasket pressure of y=17, which is 1.5 times of the specific pressure of the asbestos gasket, 11. In the embodiment of the invention, the sealing surfaces are tongue-groove surfaces. The gasket width b=(tongue width+gasket width)/2 for calculation. In the standards and the literatures, the specific pressure of the stainless steel-graphite spiral wound gasket is y=90. Based on this, after the flange gasket is changed from the asbestos gasket to the metal gasket, the bolt tightening force needs to increase by 8 times, and the flange thickness also needs to increase by 8 times. This is an obvious error, or a simple machine measurement result. Actually, after the flange gasket is changed from the asbestos gasket to the metal gasket, the bolt tightening force needs to be increased slightly but the bolts must be tightened evenly, i.e., the opposite bolts must be tightened one after another for each turn. This is a higher requirement than the asbestos gasket. The clamping chain is very easy to tighten just by tightening the bolts by force. This is one of the advantages of the hoop connector.

6. Design Calculation Result of Invention

According to the above mentioned design method of the invention, the size of the DN50˜600 hoop connector is calculated with the pressure being PN25, 40 and 63, the sealing surfaces being the tongue-groove surfaces, the gasket being the stainless steel-graphite spiral wound gasket, and the gasket thickness being 3.2. The connecting pipe designs are listed in tables 6-1, 6-2 and 6-3, and are all typical embodiments. It can be seen from the data in the tables that, the bow length margin is 13˜37 mm and the hoop connector distance is 4.7˜6.3 mm. The hoop is easy to manufacture with low requirement on the processing precision. The hoop size is obviously much smaller than the flange size, the large-caliber hoop connector does not require very thick bolts like the flange, and costs much less than the flange.

To conduct further comparison with the flange, the hoop connector weight is calculated herein. In the weight comparison of the hoop connector and the flange, the flange weight contains a pair of (two) flanges. The hoop connector weight contains a set of hoop and the conical heads of a pair of connecting pipes. When the conical heads of the connecting pipes are calculated, the outer diameters shall be used, namely, excluding the pipe used when the flange is installed. For easy description, it is called the effective conical head weight herein. The weight of the bolts and the pins of the hoop connector is less than the weight of a set of bolts of the flange. Since having low values, the bolt weight is not considered during weight comparison. The flange weight comes from the value of a welding plate flange in GB/T 9124-2010. The calculation result is listed in the table. It can be seen that the hoop connector weight is only 10˜30% of the flange weight. Larger caliber means higher pressure and larger weight difference between the hoop connector and the flange. The effective conical head weight of the connecting pipe of the hoop connector is only 2.5˜6% of the flange weight. Since the connecting pipe needs to be stainless steel and the hoop can be carbon steel (galvanized and nickel-plated) when the hoop connector is used in place of the flange, the stainless steel hoop connector is more advantages than the stainless steel flange in the price.

TABLE 6-1 Design result of hoop connector at pressure PN25 Nominal diameter DN 50 65 80 100 125 150 200 250 300 350 400 500 600 Hoop petal 4 4 4 4 6 6 8 8 8 12 12 16 16 number N Taper 15 15 15 15 15 15 15 15 12 10 10 10 10 angle α B 90 90 90 90 90 90 90 90 90 90 90 90 90 β_(w) 22.5 22.5 22.5 22.5 15 15 11.2 11.2 11.2 7.5 7.5 5.6 5.6 Γ 240 240 240 240 300 300 300 300 300 300 300 300 300 γ_(n) 60 60 60 60 50 50 37.5 37.5 37.5 25 25 18.75 18.75 Seal 9 9 9 9 9 10.5 12.5 14 14.5 16 15.5 17 17 groove width Tongue- 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 groove gap B 5.2 6.1 6.1 6.1 6.1 6.85 7.85 8.6 8.85 9.6 9.35 10.1 10.1 Connecting 20# 20# 20# 20# 20# 20# 20# 20# 20# 20# 20# 20# 20# pipe material Hoop 20# 20# 20# 20# 20# 20# 20# 20# 35# 35# 35# 35# 35# material Outer 57 76 89 108 133 159 219 273 325 377 426 530 630 diameter of pipe D_(o) Inner 50 69 82 101 126 151 207 261 311 361 410 510 610 diameter of pipe D_(i) Transition 6 6 6 7 7 8 8 10 10 10 10 10 10 arc r₁ D₁ 65.9 84.9 97.9 118.4 143.4 170.9 230.9 287.8 340.8 393.5 442.5 546.5 646.5 D_(n) 77 96 109 130 155 183 244 301 354 407 456 560 660 D_(w) 93 112 127 150 175 207 270 329 384 439 488 596 696 D_(G) 55.6 74.6 87.6 107.6 132.6 157.6 214.6 268.6 318.6 368.6 418.6 519.6 619.6 g_(D) 0.24 0.29 0.33 0.39 0.20 0.24 0.17 0.21 0.20 0.08 0.09 0.06 0.07 g_(E) 1.38 1.72 1.96 2.33 1.95 2.30 1.73 2.14 2.00 0.85 0.95 0.66 0.78 Δg 1.14 1.43 1.63 1.95 1.75 2.06 1.56 1.93 1.80 0.77 0.86 0.60 0.70 Pipe wall 3.5 3.5 3.5 3.5 3.5 4 6 6 7 8 8 10 10 thickness δ_(D) Theoretical 0.6 0.8 0.9 1.1 1.4 1.7 2.3 2.8 3.4 3.9 4.4 5.5 6.6 value Connecting 50 50 50 50 50 50 50 50 50 50 50 50 50 pipe height H Shearing 4 4 4 4 4 4 4 4 4 4 4 4 4 thickness h_(w1) h_(w2) 6 6 6 6 6 6 6 6 6 6 6 6 6 h_(n1) 5.9 5.9 6.1 6.3 6.5 7.0 8.3 8.5 8.0 8.7 8.7 9.1 9.1 h_(n2) 7.9 7.9 8.1 8.3 8.5 9.0 9.3 9.5 9.0 8.7 8.7 9.1 9.1 Theoretical 0.23 0.29 0.30 0.31 0.37 0.43 0.57 0.69 0.56 0.45 0.51 0.62 0.72 value Outer 111 130 147 170 197 229 296 355 411 467 516 626 726 diameter of hoop E_(o) Inner 101 120 136 159 185 217 280 339 395 451 500 610 710 diameter of hoop E_(i) Wall 5 5 5.5 5.5 6 6 8 8 8 8 8 8 8 thickness δ_(E) Theoretical 0.55 0.79 0.89 1.06 1.28 1.52 2.07 2.59 2.43 2.80 3.15 3.88 4.60 value Thickness 6.85 7.89 8.17 8.96 8.77 9.77 8.94 9.71 10.26 10.01 10.02 9.64 9.65 of point of tangency f_(n) Thickness 8.99 10.04 10.58 11.64 11.45 12.99 12.42 13.46 13.45 12.83 12.84 12.81 12.82 of point of tangency f_(w) Theoretical 0.19 0.25 0.25 0.27 0.33 0.38 0.51 0.63 0.41 0.34 0.38 0.47 0.55 value Hoop 32 34 35 37 37 40 40 42 42 42 42 42 42 height F Single-lug 8 8 8 10 12 12 14 16 16 16 16 22 24 bolt d₁ Theoretical 3.9 4.9 5.4 6.0 7.1 8.4 11.1 13.6 12.5 12.1 13.5 16.5 19.4 value L_(a) 20 20 20 24 26 26 30 34 34 38 41 L_(w) 25.6 27.2 28 29.6 29.6 32 32 33.6 33.6 33.6 33.6 L_(h) 6 7 7 8 10 11 13 15 15 16 18 L_(h) 3.6 4.4 4.7 5.6 6.9 7.8 11.1 14.1 12.3 12.6 14.6 theoretical value Double-lug 6 6 6 8 10 10 12 14 14 14 14 14 16 bolt d₁ Theoretical 2.8 3.5 3.8 4.3 5.0 5.9 7.9 9.6 8.8 8.5 9.5 11.7 13.7 value L_(a) 17 17 17 20 25 25 27 30 30 30 30 33 33 L_(w) 18 18 18 23 28 28 32 37 37 37 37 37 42 L_(h) 6 7 7 7 8 8 10 11 11 11 12 13 14 L_(h) 2.8 3.5 3.8 4.1 4.9 5.8 7.4 8.9 7.8 7.5 8.4 10.8 11.9 theoretical value Pin 6 6 6 8 8 8 10 10 10 10 10 12 14 diameter d₃ Theoretical 2.1 2.6 2.8 3.2 3.8 4.4 5.9 7.2 6.3 6.1 6.8 8.3 9.8 value Ear 12 12 12 15 17 17 20 20 20 20 20 22 24 diameter d₅ Theoretical 7.0 7.2 7.3 9.7 10.0 10.4 13.7 14.9 14.0 13.8 14.5 18.4 22.6 value Bow 2.5 2.4 2.4 2.4 3.1 3.1 3.1 3.1 3.2 3.2 3.2 3.2 3.2 length ratio ω Bow 13.5 13.8 15.7 18.7 22 25.9 26.6 32.9 38.8 30.2 33.9 31.4 37.1 length margin ΔC Hoop 4.7 4.5 4.3 4.4 5.1 5.2 5.9 5.8 5.7 6.3 6.2 6.4 6.3 connector margin ΔL Flange 5.46 6.96 8.64 12.14 16.38 20.6 28.6 40.2 53.2 83.6 115.2 174 254 weight kg Hoop 1.66 2.19 2.90 3.97 5.03 7.32 11.6 16.6 19.5 22.8 26.3 38.7 48.5 weight kg Hoop 30.5 31.5 33.6 32.7 30.7 35.5 40.6 41.3 36.7 27.2 22.8 22.3 19.1 connector/ flange weight % Conical 8.7 8.6 8.6 8.4 7.4 8.4 9.4 9.4 8.2 6.4 5.2 4.6 3.7 head/flange weight %

TABLE 6-2 Design result of hoop connector at pressure PN40 Nominal diameter DN 50 65 80 100 125 150 200 250 300 350 400 500 600 Hoop petal 4 4 4 4 6 6 8 8 8 12 12 16 16 number N Connecting 20# 20# 20# 20# 20# 20# 20# 20# 20# 20# 20# 20# 20# Pipe material Hoop 35# 35# 35# 35# 35# 35# 35# 35# 35# 35# 35# 30CrMo 30CrMo material Pipe wall 3.5 3.5 3.5 3.5 3.5 4 6 6 7 8 8 10 12 thickness δ_(D) Theoretical 0.92 1.2 1.4 1.8 2.2 2.6 3.6 4.4 5.3 6.1 6.9 8.6 10.2 value Connecting 50 50 50 50 50 50 50 50 50 50 50 50 50 pipe height H Shearing 4 4 4 4 4 4 4 4 4 4 4 4 4 thickness h_(w1) h_(w2) 6 6 6 6 6 6 6 6 6 6 6 6 6 h_(n1) 5.9 5.9 6.1 6.3 6.5 7.0 8.3 8.5 8.0 8.7 8.7 9.1 9.1 h_(n2) 7.9 7.9 8.1 8.3 8.5 9.0 9.3 9.5 9.0 8.7 8.7 9.1 9.1 Theoretical 0.36 0.45 0.47 0.49 0.58 0.68 0.90 1.09 0.88 0.72 0.80 0.97 1.14 value Outer 111 130 147 170 197 229 296 355 411 467 516 626 726 diameter of hoop E_(o) Inner 101 120 136 159 185 217 280 339 395 451 500 610 710 diameter of hoop E_(i) Wall 5 5 5.5 5.5 6 6 8 8 8 8 8 8 8 thickness δ_(E) Theoretical 0.70 1.00 1.13 1.34 1.62 1.92 2.62 3.27 3.81 4.40 4.95 5.02 5.95 value Thickness 6.85 7.89 8.17 8.96 8.77 9.77 8.94 9.71 10.26 10.01 10.02 9.64 9.65 of point of tangency f_(n) Thickness 8.99 10.04 10.58 11.64 11.45 12.99 12.42 13.46 13.45 12.83 12.84 12.81 12.82 of point of tangency f_(w) Theoretical 0.24 0.31 0.32 0.34 0.41 0.48 0.65 0.80 0.65 0.53 0.60 0.60 0.71 value Hoop 32 34 35 37 37 40 40 42 42 42 42 42 42 height F Single-lug 8 8 8 10 12 14 18 18 18 18 bolt d₁ Theoretical 4.7 5.9 6.3 7.1 8.4 9.9 13.1 16.1 15.7 15.2 16.9 16.1 18.9 value L_(a) 20 20 20 24 26 30 38 38 38 38 L_(w) 25.6 27.2 28 29.6 29.6 32 32 33.6 33.6 33.6 L_(h) 6 7 7 8 10 11 13 20 20 20 L_(h) 4.0 4.9 5.2 6.3 7.7 9.4 14.0 16.8 16.3 15.8 theoretical value Double-lug 3.3 4.1 4.5 5.0 6.0 7.0 9.3 11.4 11.1 10.7 12.0 11.4 13.4 bolt d₁ Theoretical 6 6 6 8 10 10 14 14 14 14 14 14 18 value L_(a) 17 17 17 20 25 25 27 30 30 30 30 33 37 L_(w) 18 18 18 23 28 28 32 37 37 37 37 37 42 L_(h) 6 7 7 7 8 8 10 11 11 11 12 14 16 L_(h) 3.1 3.9 4.3 4.6 5.5 6.5 8.4 10.1 9.8 9.5 10.6 12.3 14.4 theoretical value Pin 6 6 6 8 8 8 10 10 10 10 10 12 14 diameter d₃ Theoretical 2.4 3.0 3.2 3.6 4.3 5.0 6.6 8.1 7.9 7.7 8.5 9.5 11.1 value Ear 12 12 12 15 17 17 20 20 20 20 20 22 24 diameter d₅ Theoretical 7.1 7.4 7.5 9.9 10.3 10.8 14.4 16.0 15.7 15.4 16.5 19.9 24.7 value Flange 5.46 6.96 8.64 12.14 16.38 21.6 35.8 59.6 90.2 133.4 194.2 weight kg Hoop 1.66 2.19 2.90 3.97 5.03 7.32 11.62 16.60 19.55 22.77 26.29 38.75 48.54 weight kg Hoop 30.5 31.5 33.6 32.7 30.7 33.9 32.4 27.9 21.7 17.1 13.5 connector/ flange weight % Conical 8.7 8.6 8.6 8.4 7.4 8.0 7.5 6.3 4.9 4.0 3.1 head/flange weight %

TABLE 6-3 Design result of hoop connector at pressure PN63 Nominal diameter DN 50 65 80 100 125 150 200 250 300 350 400 500 600 Hoop petal 4 4 4 4 6 6 8 8 8 12 12 16 16 number N Connecting 20# 20# 20# 20# 20# 20# 20# 20# 20# 20# 20# 20# 20# pipe material Hoop 35# 35# 35# 35# 35# 35# 35# 35# 35# 35# 35# 30CrMo 30CrMo material Pipe wall 3.5 3.5 3.5 3.5 4 6 8 8 8 10 10 14 14 thickness δ_(D) Theoretical 1.4 1.9 2.2 2.7 3.3 4.0 5.4 6.8 6.6 7.6 8.6 10.7 12.7 value Connecting 50 50 50 50 50 50 50 50 50 50 50 50 50 pipe height H Shearing 4 4 4 4 4 4 4 4 4 4 4 4 4 thickness h_(w1) h_(w2) 6 6 6 6 6 6 6 6 6 6 6 6 6 h_(n1) 5.9 5.9 6.1 6.3 6.5 7.0 8.3 8.5 8.0 8.7 8.7 9.1 9.1 h_(n2) 7.9 7.9 8.1 8.3 8.5 9.0 9.3 9.5 9.0 8.7 8.7 9.1 9.1 Theoretical 0.56 0.70 0.73 0.77 0.90 1.03 1.34 1.64 1.08 0.89 1.00 1.24 1.45 value Outer 111 130 147 170 197 229 296 355 411 467 516 626 726 diameter of hoop E_(o) Inner 101 120 136 159 185 217 280 339 395 451 500 610 710 diameter of hoop E_(i) Wall 5 5 5.5 5.5 6 6 8 8 8 8 8 8 8 thickness δ_(E) Theoretical 0.70 1.00 1.13 1.34 1.62 1.92 2.62 3.27 3.81 4.40 4.95 5.02 5.95 value Thickness 6.85 7.89 8.17 8.96 8.77 9.77 8.94 9.71 10.26 10.01 10.02 9.64 9.65 of point of tangency f_(n) Thickness 8.99 10.04 10.58 11.64 11.45 12.99 12.42 13.46 13.45 12.83 12.84 12.81 12.82 of point of tangency f_(w) Theoretical 0.37 0.49 0.50 0.54 0.64 0.73 0.97 1.20 0.82 0.68 0.77 0.96 1.13 value Hoop 32 34 35 37 37 40 40 42 42 42 42 42 42 height F Single-lug 8 10 10 12 14 16 20 24 18 18 bolt d₁ Theoretical 5.8 7.3 7.9 8.9 10.5 12.2 16.1 19.7 15.1 14.7 16.4 20.3 23.8 value L_(a) 20 20 20 24 26 30 38 38 38 38 L_(w) 25.6 27.2 28 29.6 29.6 32 32 33.6 33.6 33.6 L_(h) 6 7 7 8 10 11 13 20 20 20 L_(h) 5.0 6.1 6.6 7.8 9.6 11.6 17.2 20.5 18.3 17.9 theoretical value Double-lug 6 6 6 8 10 10 14 16 14 14 14 18 20 bolt d₁ Theoretical 4.1 5.2 5.6 6.3 7.4 8.6 11.4 14.0 10.6 10.4 11.6 14.4 16.8 value L_(a) 17 17 17 20 25 25 30 33 31 31 31 36 40 L_(w) 18 18 18 23 28 28 37 42 37 37 37 47 52 L_(h) 6 7 7 7 8 10 13 14 13 14 14 16 18 L_(h) 3.9 4.9 5.3 5.7 6.9 8.0 10.0 12.1 11.2 10.9 12.2 14.4 16.9 theoretical value Pin 6 6 6 8 8 8 10 12 12 12 12 14 16 diameter d₃ Theoretical 2.9 3.7 4.0 4.5 5.3 6.2 8.1 10.0 8.9 8.6 9.7 12.0 14.0 value Ear 12 12 12 15 17 17 20 22 22 22 22 28 34 diameter d₅ Theoretical 7.4 7.9 8.0 10.5 11.2 11.8 16.2 20.6 19.1 18.8 20.2 26.1 32.3 value Flange 3.99 4.73 5.9 8.05 11.7 16.9 20.5 42.1 59.1 88.7 121 weight kg Hoop 1.66 2.19 2.9 3.97 5.03 7.32 11.6 16.6 19.5 22.7 26.3 40.2 51.8 weight kg Hoop 20.8 23.2 24.6 24.7 21.5 21.7 28.3 19.7 16.5 12.8 10.9 connector/ flange weight % Conical 6.0 6.4 6.3 6.3 5.2 5.1 6.6 4.5 3.7 3.0 2.5 head/flange weight %

7. Embodiments:

1) A DN100PN25 hoop connector, manufactured according to Table 6-1, at the test water pressure of 5 MPa maintained for 24 hours without leakage.

2) A DN150PN40 hoop connector, manufactured according to Table 6-2, at the test water pressure of 10 MPa maintained for 24 hours without leakage.

The above description is preferred embodiments of the invention only. It shall be pointed out that many improvements and modifications can be made by one of ordinary skill in the technical field without departing from the principle of the invention, which shall also be regarded as falling within the scope of protection of the invention. 

1. A multi-petaled oblique-plane hoop, characterized in that the hoop is divided into two sub-assembly groups, and hoop petals in each sub-assembly group are connected by pins, and the pins are parallel to a connecting pipe shaft the sub-assembly groups are connected by using bolts, and the bolts are vertical to the connecting pipe shaft each hoop petal is in a shape of a partial ring stud, in which an arc-shaped groove is formed an upper surface and the lower surface of the groove are symmetrical form partial inner cone surfaces, and the hoop petals are connected to form a clamping chain.
 2. The hoop according to claim 1, characterized in that the taper angle of the inner cone surface of the hoop petal, and the included angle between the normal direction of the inner cone surface and the axial direction of the clamping chain is α=10˜20°; the hoop petal number N is an even number, which is not higher than the number of the bolts of the flanges of the same caliber.
 3. The hoop according to claim 1, characterized in that the inner cone surface of each hoop petal is convex in the middle to form a trapezoidal plane which is parallel to the cone surface and the oblique angle of the plane is equal to the taper angle of the cone surface.
 4. The hoop according to claim 1, characterized in that the sum of the trapezoid angles γ formed by extending the two sides of the trapezoidal plane of each hoop petal to the center of circle of the clamping chain is Γ=180˜300°, and the trapezoid angle of a single hoop petal is γ=Γ/N.
 5. A connecting pipe, matching the hoop according to claim 1, characterized in that one end of the pipe connector is a pipe head, the other end thereof is a convex conical head, the pipe head is welded with the pipe, the outer taper angle of the conical head is equal to the inner taper angle of the hoop petal, and concave trapezoidal oblique planes parallel to the outer cone surface of the conical head are formed on the outer cone surface.
 6. The connecting pipe according to claim 5, characterized in that the sum of the trapezoid angles formed by extending the two sides of the trapezoidal oblique plane on the conical head of the connecting pipe to the center of circle of the connecting pipe is B=90˜120°, and the ratio of the trapezoidal angle of the hoop petal to the trapezoidal angle of the connecting pipe is γ/β≥2.
 7. The connecting pipe according to claim 5, characterized in that the bottom surface of the conical head of the connecting pipe is a sealed surface with a forced seal gasket with the sealed surface being a plane, a concave-convex surface, a tongue-groove surface, a ring groove surface or a triangular-ring inner groove surface, or with a soft seal gasket with self-tightening function.
 8. The connecting pipe according to claim 5, characterized in that the pipe head of the connecting pipe is connected with the pipe through thread.
 9. A pipe connector, composed of the clamping chain as stated in claim 1 and a connecting pipe, characterized in that one end of the pipe connector is a pipe head, the other end thereof is a convex conical head, the pipe head is welded with the pipe, the outer taper angle of the conical head is equal to the inner taper angle of the hoop petal, and concave trapezoidal oblique planes parallel to the outer cone surface of the conical head are formed on the outer cone surface; wherein a set of clamping chain and a pair of connecting pipes form a set of pipe connector, a seal gasket is placed between the conical heads of the two connecting pipes, and the pipe heads of the two connecting pipes are respectively welded with the pipes on the two sides or connected with the latter through thread.
 10. The pipe connector according to claim 9, characterized in that the pipe connector is used for valve production, and the flange on a traditional flange-connected valve is replaced with the connecting pipe, and the valve is connected with the pipe through the clamping chain; the connecting pipe has a caliber DN of DN50˜700. 